Algorithm that creates new images based on other images
I'm not an expert on that so you could probably get a better answer.

I'm not sure to understand what you're looking for. Are the couple of images about the same thing? Like pictures of cats and you want to generate a new cat based on these pictures? If that's what you want, you could probably take a look at Generative Adversarial Network (GAN) : Introduction.
A GAN is made up of a Generator and a Discriminator. The goal of the discriminator is to distinguish the real data from the generated data. And the goal of the generator is to improve its generated data to look similar to real data. Then, if there are different cat images in your dataset, the generator will learn to create a new cat based on that dataset.

If what you're looking for is to take different images like a cat and a dog and generate a "catdog", you can take a look at Variational AutoEncoder (VAE). For example you can train two different VAE (Encoder/Decoder). One for cats, and one for dogs. Then you take the encoder of dogs and the decoder of cats. That what I saw one day, not sure if it really works.

Correct me if I'm wrong